Our work in this section is motivated by the work of Huneke and Wiegand [1]}. The main purpose of this section is to obtain some new criteria for the freeness of modules in terms of the vanishing of local cohomology. Along the way, as an application, we obtain a new splitting criteria - for an arithmetically Cohen-Macaulay vector bundle on a smooth complete intersection of an odd dimension – in terms of the cohomological rigidity property; see Corollary REF .
